In terms of specific reasons to doubt the Gaza Health Ministry numbers specifically, I could go on forever about that, but I don't see the point of doing so on HN. It's not a tech-related question.
Regardless, our (USA) parties are in fact the biggest blockers to our functioning correctly as a liberal democracy. One is desperate for votes from anyone, the other party is terrified to pass anything or imagine any kind of future that isn't a slightly less grim version of what the republicans offer. Just by our ability to come to a consensus and do things as a country, we seem to have ground to a complete halt. So yea, people should be a lot more critical of whether or not we're actually espousing the democratic ideals we claim.
I do not agree with Israel's policies on the West Bank, but the issue is more complicated than I suspect you think and I encourage you to read Israeli perspectives on it.
Pro-Palestinian rhetoric on this site goes off the rails in so many directions, and because it seems to be the majority opinion on the site, there are many more examples of off-the-rails comments from that side. But this assertion of Gaza's independence from Israel is one of the reliable off-the-rails pro-Israel sentiments I see here.
Gaza was blockaded. Israel tried to control who and what goes in and out of Gaza (to try to limit the weapons Hamas has). But Israel had no control over what the Hamas Gaza government did in Gaza, how they spent their budget, what they built, what they taught in schools, what their military was planning.
It would be a "breakaway province" situation, except that:
a. Israel intentionally got all its citizens out of that place and
b. Israel had no intention of taking control and forcing Gaza to join back into Israel.
Israel mistakenly thought Hamas was transforming into a national government that is busy governing its territory.
Gaza was mostly an independent country at war with Israel and not even a little bit an autonomous province of Israel. The war could not be resolved and so it was stuck in a state where Israel thought it prevented Hamas from bringing in heavy weapons but did not want to commit to conquering a city.
I think some people thought that after Israel pulled out in 2005, and Gaza became autonomous, it would become a normal independent country, and people still treat Gaza of 2023 as if it's the Gaza of 2005.
I think if someone is going to raise the "Gaza isn't Israel it's an independent country" argument, the facts lining up against an natural reading of that kind of statement make it incumbent on the speaker to lay out the qualifications and contingencies, rather than counting on other speakers on the thread to do it for them. It's not a thing you can just say and pretend is clear; it's more or less an extraordinary claim.
I'd entertain the argument if someone wanted to explore it in a curious fashion. But, like, it's not true. Gaza is occupied territory in the intuitive meaning of the term.